A tomogram is a two-dimensional image of a slice or section through a three-dimensional object. A tomograph is the apparatus for generating a tomogram. Tomography is the entire process to produce a tomogram. Computed Tomography (CT) is the entire process to produce a tomogram where the computation is performed by a computer.
CT is composed of two major steps or processes. The first is scanning a three dimensional object and the second is computing tomograms of the scanned body. Multiple tomograms are combined to produce a three dimensional density map or volume representation of the scanned object.
A typical CT scan system is formed of a radiation source, such as an x-ray tube, a radiation detector, and a computer system. The radiation source and detector are positioned on opposite sides of an object to image. A beam of radiation is then projected from the source towards the detector, and those photons not absorbed by the object are transmitted toward and impact on the detector. The result is an image on the detector that represents a two-dimensional projection image of the tree-dimensional object from the current position of the x-ray source. The source and detector are typically rotated around the object 180° or 360°, during which the imaging process is repeated at a number of intermediate positions, so that a series of two-dimensional images of the object over a range of angular orientations is acquired. A CT scan system can also scan an object using a set of fixed x-ray sources and detectors that surround the object so that neither the x-ray source, nor the detector is moved. A CT scan can be performed with the body at rest or in motion perpendicular to the scanning apparatus. The latter case results in a helical scan.
A series of these projection images from the detector is fed into a computer system. The computer system can use these two-dimensional projections to create various reconstructions of the object. This concept is known as tomographic volume reconstruction. A variety of mathematical algorithms, including but not limited to, Feldkamp back-projection, algebraic reconstruction technique (ART), and maximum likelihood expectation maximization (MLEM), can be used in connection with tomographic volume reconstruction. Most algorithms are based on the assumption that a large number of projection measurements are made, such that every point in the object is included in radiation paths from many angles. Feldkamp back-projection is a reconstruction technique in which projection data is first convolved with a filter, and each view is successively superimposed over a square grid, which represents the volume that was imaged, at an angle that corresponds to angle of the x-ray source at the moment of acquisition. During the process of superimposition or accumulation, the perspective geometry must be known to obtain the location of the projection of each element of the grid onto the detector, and a multiplicative weight factor must also be known and applied to the value from the filtered detector data.
The perspective geometry and the multiplicative weight factor require evaluating computationally expensive transcendental functions. For some CT scan systems these calculations are further complicated because the weight factors and perspective geometry cannot be determined by analytic functions and must be determined by using a priori knowledge of the location of the x-ray source and detector. In either case the perspective geometry and the weight factors can be pre-computed and stored in memory. For some scanners the array of detectors and X-Ray source are constructed to be perfectly symmetric across one or two axes. By exploiting these geometric symmetries the size of the tables for weight factors and geometry can be reduced.
For CT scans where the object is moving, if the motion through the scanner is coordinated appropriately with the production of the projections, the weight computation will also be repetitive over some cyclic interval; thus allowing the weight tables and the perspective geometry to be pre-computed as is the case for CT scan of a stationary object.
Even if symmetries in the scanner geometry can be leveraged to reduce the table size, these tables can become very large and the memory storage and memory access bandwidth requirements can adversely impact the performance of the reconstruction system.
It is therefore an object of this invention to provide an improved method for the storage and access of the pre-computed tables for back-projection reconstruction in CT. This method results in a faster and/or less expensive CT computer system for performing reconstruction using back-projection techniques.